Consider a spherical wave Show that E obeys maxwell's equations

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Homework Statement

Consider a simple spherical wave, with omega/k=c

E(r, theta, phi, t)=((A sin theta)/r)(cos(kr - omega t) -(1/kr)sin(kr - omega t)) phi-hat

i) Using Faraday's law, find the associated magnetic field B
ii) Show that E obeys the remaining three of Maxwell's equations

The Attempt at a Solution

It's part b I am stuck on. I tried to prove it obeys div E=ro/epsilon0

I tried to do div E in spherical coordinates but I don't know how to when I don't know how to differentiate it with respect to phi because the equation given for E doesn't contain phi. i also don't know how ro is related to any of the terms in the equation for E. Please help.

 

[dextercioby]

If it doesn't contain phi, then obviously the derivative of E wrt it is 0...

 

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I am now stuck on proving that the wave obey's the Ampere-Maxwell law. I tried to prove that curl B=0. It doesn't. Did I make a mistake in calculating, or is this the wrong approach to take to the question?

 

[dextercioby]

What is B equal to ?